System and method for predictive analysis of 2-dimensional crystal structures

Abstract

The present invention provides a system and method for applying Siamese Neural Networks (“SNNs”) to model, characterize, and predict the effects of defects on material properties, specifically for 2-dimensional (“2D”) crystals such as transition metal dichalcogenides (“TMDCs”). The present invention provides a method for predicting physical properties with strong performance across both low and high-defect density scenarios.

What is claimed is: 
     
         1 . A system for predicting physical properties of two-dimensional crystals with defect configurations, comprising:
 at least one machine learning model used to generate invariant embeddings of defect configurations in two-dimensional crystal lattices;   said at least one machine learning model applying a training methodology to defect recognition;   a Siamese Neural Network (SNN) trained on labeled pairs of defect placements, wherein said labeled pairs of defect placements comprise positive pairs representing identical configurations derived through symmetry operations and negative pairs representing distinct configurations with similar base descriptors; and   a distance-based loss function configured to optimize said embeddings for classification accuracy;   a base descriptor computationally generated for defect configurations in two-dimensional crystal lattices;   a convolutional neural network architecture utilizing circular padding to ensure consistent feature representation during periodic translations of input data, enhancing invariance to defect placements;   a predictor of physical properties of two-dimensional materials;   a retrieval of lattice configurations based on said embeddings;   a generalized approach for invariant embedding generation that applies to various two-dimensional materials and accommodates different defect densities; and   a designing of two-dimensional crystal structures.   
     
     
         2 . The system of  claim 1 , wherein said machine learning model includes:
 utilizing said SNN to create embeddings invariant to symmetry operations such as translation, rotation, and reflection specific to a lattice structure; and   employing a contrastive learning framework to ensure embeddings of equivalent configurations are close in an embedding space, while non-equivalent configurations are distant.   
     
     
         3 . The system of  claim 1 , wherein said base descriptor computationally generated includes:
 counting defect occurrences across lattice layers and types; and   applying symmetry-based transformations to ensure descriptor invariance under reflection or rotation.   
     
     
         4 . The system of  claim 1 , wherein said training methodology includes:
 initial training with a balanced dataset of positive and negative pairs;   identifying hard negatives and incorporating them into a training dataset for enhanced discrimination.   
     
     
         5 . The system of  claim 1 , wherein said predictor of physical properties of two-dimensional materials includes:
 mapping invariant embeddings to target physical properties, including formation energy and electronic bandgap; and   employing a multi-layer perceptron (MLP) for downstream tasks, trained on embeddings augmented with polynomial features for enhanced predictive accuracy.   
     
     
         6 . The system of  claim 1 , wherein said retrieval of lattice configurations based on embeddings includes:
 a K-D tree utilized for efficient nearest-neighbor searches in an embedding space; and   enabling rapid identification of configurations with desired properties.   
     
     
         7 . The system of  claim 1 , wherein said generalized approach for invariant embedding generation that applies to various two-dimensional materials and accommodates different defect densities further by:
 standardizing input representations; and   preserving invariance under symmetry operations regardless of defect count.   
     
     
         8 . The system of  claim 1 , wherein said designing of two-dimensional crystal structures includes:
 mapping desired physical property ranges to specific defect configurations using a learned embedding space; and   employing generative models trained on embeddings to propose new configurations.   
     
     
         9 . A method for generating invariant embeddings of defect configurations in two-dimensional crystal lattices using a machine learning model, the method comprising:
 utilizing a neural network to create embeddings invariant to symmetry operations specific to a lattice structure;   employing a contrastive learning framework to ensure embeddings of equivalent configurations are close in an embedding space, while non-equivalent configurations are distant;   generating invariant embeddings of defect configurations in two-dimensional crystal lattices using a machine learning model;   training a Siamese Neural Network on labeled pairs of defect placements;   optimizing said embeddings for classification accuracy through a distance-based loss function;   computationally generating a base descriptor for defect configurations in two-dimensional crystal lattices;   training for machine learning models applied to defect recognition;   utilizing circular padding within a convolutional neural network architecture to ensure consistent feature representation during periodic translations of input data, enhancing invariance to defect placements;   predicting physical properties of two-dimensional materials;   retrieving lattice configurations based on embeddings;   applying invariant embedding generation to various two-dimensional materials and accommodates different defect densities; and   designing two-dimensional crystal structures for generation.   
     
     
         10 . The method of  claim 9 , wherein said symmetry operations include translation, rotation, and reflection. 
     
     
         11 . The method of  claim 10 , wherein said machine learning model includes:
 utilizing a neural network to create embeddings invariant to symmetry operations such as translation, rotation, and reflection specific to a lattice structure; and   employing a contrastive learning framework to ensure embeddings of equivalent configurations are close in an embedding space, while non-equivalent configurations are distant.   
     
     
         12 . The method of  claim 10 , wherein said Siamese Neural Network includes:
 positive pairs representing identical configurations derived through symmetry operations; and   negative pairs representing distinct configurations with similar base descriptors.   
     
     
         13 . The method of  claim 10 , wherein said base descriptor computationally generated includes:
 counting defect occurrences across lattice layers and types; and   applying symmetry-based transformations to ensure descriptor invariance under reflection or rotation.   
     
     
         14 . The method of  claim 10 , wherein a training methodology includes:
 initial training with a balanced dataset of positive and negative pairs; and   identifying hard negatives and incorporating them into a training dataset for enhanced discrimination.   
     
     
         15 . The method of  claim 10 , wherein a predictor of physical properties of two-dimensional materials includes:
 mapping invariant embeddings to target physical properties, including formation energy and electronic bandgap; and   employing a multi-layer perceptron (MLP) for downstream tasks, trained on embeddings augmented with polynomial features for enhanced predictive accuracy.   
     
     
         16 . The method of  claim 10 , wherein a retrieval of lattice configurations based on embeddings includes:
 a K-D tree utilized for efficient nearest-neighbor searches in an embedding space; and   enabling rapid identification of configurations with desired properties.   
     
     
         17 . The method of  claim 10 , wherein a generalized approach for invariant embedding generation that applies to various two-dimensional materials and accommodates different defect densities further by:
 standardizing input representations; and   preserving invariance under symmetry operations regardless of defect count.   
     
     
         18 . The method of  claim 10 , wherein a designing of two-dimensional crystal structures includes:
 mapping desired physical property ranges to specific defect configurations using a learned embedding space; and   employing generative models trained on embeddings to propose new configurations.   
     
     
         19 . A system for predicting physical properties of two-dimensional crystals with defect configurations, comprising:
 at least one machine learning model used to generate invariant embeddings of defect configurations in two-dimensional crystal lattices;   said at least one machine learning model applying a training methodology to defect recognition;   a Siamese Neural Network trained on labeled pairs of defect placements;   a distance-based loss function to optimize the embeddings for classification accuracy;   a base descriptor computationally generated for defect configurations in two-dimensional crystal lattices;   a convolutional neural network architecture utilizing circular padding to ensure consistent feature representation during periodic translations of input data, enhancing invariance to defect placements;   wherein said convolutional neural network architecture includes three convolutional layers and three fully connected layers;   a predictor of physical properties of two-dimensional materials;   a retrieval of lattice configurations based on embeddings;   a generalized approach for invariant embedding generation that applies to various two-dimensional materials and accommodates different defect densities;   wherein application and accommodation includes standardizing input representations and preserving invariance under symmetry operations regardless of defect count;   a designing of two-dimensional crystal structures; and   an ability to enhance a classification of defect configurations by concatenating a base descriptor of defects, embeddings generated from multiple stages of neural network processing; and distinct components derived from hierarchical training.   
     
     
         20 . The system of  claim 19 , wherein a final embedding is constructed in three parts, comprising:
 a first part constructed via the base descriptor of a configuration; and   a second part and a third part deriving from a tensor of the configuration.